List of manifolds

This is a list of particular manifolds, by Wikipedia page. See also list of geometric topology topics. For categorical listings see Category:Manifolds and its subcategories.

Generic families of manifolds

 * Euclidean space, Rn
 * n-sphere, Sn
 * n-torus, Tn
 * Real projective space, RPn
 * Complex projective space, CPn
 * Quaternionic projective space, HPn
 * Flag manifold
 * Grassmann manifold
 * Stiefel manifold

Lie groups provide several interesting families. See Table of Lie groups for examples. See also: List of simple Lie groups and List of Lie group topics.

1-manifolds

 * Circle, S1
 * Long line
 * Real line, R
 * Real projective line, RP1 ≅ S1

2-manifolds

 * Cylinder, S1 × R
 * Klein bottle, RP2 # RP2
 * Klein quartic (a genus 3 surface)
 * Möbius strip
 * Real projective plane, RP2
 * Sphere, S2
 * Surface of genus g
 * Torus
 * Double torus

3-manifolds

 * 3-sphere, S3
 * 3-torus, T3
 * Poincaré homology sphere
 * SO(3) ≅ RP3
 * Solid Klein bottle
 * Solid torus
 * Whitehead manifold
 * Meyerhoff manifold
 * Weeks manifold

For more examples see 3-manifold.

4-manifolds

 * Complex projective plane
 * Del Pezzo surface
 * E8 manifold
 * Enriques surface
 * Exotic R4
 * Hirzebruch surface
 * K3 surface

For more examples see 4-manifold.

Manifolds related to spheres

 * Brieskorn manifold
 * Exotic sphere
 * Homology sphere
 * Homotopy sphere
 * Lens space
 * Spherical 3-manifold

Special classes of Riemannian manifolds

 * Einstein manifold
 * Ricci-flat manifold
 * G2 manifold
 * Kähler manifold
 * Calabi–Yau manifold
 * Hyperkähler manifold
 * Quaternionic Kähler manifold
 * Riemannian symmetric space
 * Spin(7) manifold

Manifolds definable by a particular choice of atlas

 * Affine manifold
 * Analytic manifold
 * Complex manifold
 * Differentiable (smooth) manifold
 * Piecewise linear manifold
 * Lipschitz manifold
 * Topological manifold

Manifolds with additional structure

 * Almost complex manifold
 * Almost symplectic manifold
 * Calibrated manifold
 * Complex manifold
 * Contact manifold
 * CR manifold
 * Finsler manifold
 * Hermitian manifold
 * Hyperkähler manifold
 * Kähler manifold
 * Lie group
 * Pseudo-Riemannian manifold
 * Riemannian manifold
 * Sasakian manifold
 * Spin manifold
 * Symplectic manifold

Infinite-dimensional manifolds

 * Banach manifold
 * Fréchet manifold
 * Hilbert manifold